First, multiply each side of the equation by #color(red)(60)# to eliminate the fraction and keep the equation balanced. Eliminating the fraction will make solving the problem easier to do. #color(red)(6)# is the lowest common denominator of the two fractions.
#color(red)(60)(k - 5/12) = color(red)(60) xx -3/10#
#(color(red)(60) xx k) - (color(red)(60) xx 5/12) = cancel(color(red)(60))6 xx -3/color(red)(cancel(color(black)(10)))#
#60k - (cancel(color(red)(60))5 xx 5/color(red)(cancel(color(black)(12)))) = -18#
#60k - 25 = -18#
Next, add #color(red)(25)# to each side of the equation to isolate the #k# term while keeping the equation balanced:
#60k - 25 + color(red)(25) = -18 + color(red)(25)#
#60k - 0 = 7#
#60k = 7#
Now, divide each side of the equation by #color(red)(60)# to solve for #k# while keeping the equation balanced:
#(60k)/color(red)(60) = 7/color(red)(60)#
#(color(red)(cancel(color(black)(60)))k)/cancel(color(red)(60)) = 7/60#
#k = 7/60#
